There is a WinInet API in Windows, that I believe the .Net class is just a wrapper for. I don't remember any of the functions offhand, though.
Another alternative is to use plain sockets and do all the HTTP/FTP protocol work yourself. More work, but it's a good learning experience. You can find the HTTP and FTP protocols in one of the many RFCs available. (Search
http://www.faqs.org/rfcs, or look at
RFC 3600 for a list of RFCs covering various protocols.)